Symmetry Breaking For Representations Of Rank One Orthogonal Groups (memoirs Of The American Mathematical Society)
by Toshiyuki Kobayashi /
2015 / English / PDF
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The authors give a complete classification of intertwining
operators (symmetry breaking operators) between spherical principal
series representations of $G=O(n+1,1)$ and $G'=O(n,1)$. They
construct three meromorphic families of the symmetry breaking
operators, and find their distribution kernels and their residues
at all poles explicitly. Symmetry breaking operators at exceptional
discrete parameters are thoroughly studied. The authors obtain
closed formulae for the functional equations which the composition
of the symmetry breaking operators with the Knapp--Stein
intertwining operators of $G$ and $G'$ satisfy, and use them to
determine the symmetry breaking operators between irreducible
composition factors of the spherical principal series
representations of $G$ and $G'$. Some applications are included.
The authors give a complete classification of intertwining
operators (symmetry breaking operators) between spherical principal
series representations of $G=O(n+1,1)$ and $G'=O(n,1)$. They
construct three meromorphic families of the symmetry breaking
operators, and find their distribution kernels and their residues
at all poles explicitly. Symmetry breaking operators at exceptional
discrete parameters are thoroughly studied. The authors obtain
closed formulae for the functional equations which the composition
of the symmetry breaking operators with the Knapp--Stein
intertwining operators of $G$ and $G'$ satisfy, and use them to
determine the symmetry breaking operators between irreducible
composition factors of the spherical principal series
representations of $G$ and $G'$. Some applications are included.
